Ex 11.1, 5 - Chapter 11 Class 10 Areas related to Circles

Last updated at April 16, 2024 by Teachoo

Transcript

Ex 11.1, 5
In a circle of radius 21 cm, an arc subtends an angle of 60Β° at the centre. Find:
the length of the arc
Length of Arc APB = π½/πππ Γ (ππ π)
= (60Β°)/(360Β°) Γ 2 Γ 22/7 Γ 21
= 1/6 Γ 2 Γ 22 Γ 3
= 22 cm
Ex 11.1, 5
In a circle of radius 21 cm, an arc subtends an angle of 60Β° at the centre. Find:
(ii) area of the sector formed by the arc
Area of sector OAPB = π/360Γππ2
= ππ/πππ Γ ππ/π Γ ππ Γ ππ
= 1/6 Γ 22/7 Γ 21 Γ 21
= 1/6 Γ 22 Γ 3 Γ 21
= 231 cm2
Ex 11.1, 5
In a circle of radius 21 cm, an arc subtends an angle of 60Β° at the centre. Find:
(iii) area of segment formed by the corresponding chord
Area of segment APB
= Area of sector OAPB β Area of ΞOAB
From last part,
Area of sector OAPB = 231 cm2
Finding area of Ξ AOB
Area Ξ AOB = 1/2 Γ Base Γ Height
We draw OM β₯ AB
β΄ β OMB = β OMA = 90Β°
And, by symmetry
M is the mid-point of AB
β΄ BM = AM = 1/2 AB
In right triangle Ξ OMA
sin O = (side opposite to angle O)/Hypotenuse
sin ππΒ° = ππ΄/π¨πΆ
1/2=π΄π/21
21/2 = AM
AM = ππ/π
In right triangle Ξ OMA
cos O = (π πππ ππππππππ‘ π‘π πππππ π)/π»π¦πππ‘πππ’π π
cos ππΒ° = πΆπ΄/π¨πΆ
β3/2=ππ/21
β3/2 Γ 21 = OM
OM = βπ/π Γ 21
From (1)
AM = π/πAB
2AM = AB
AB = 2AM
Putting value of AM
AB = 2 Γ 1/2 Γ 21
AB = 21cm
Now,
Area of Ξ AOB = 1/2 Γ Base Γ Height
= π/π Γ AB Γ OM
= 1/2 Γ 21 Γ β3/2 Γ 21
= (πππβπ)/π cm2
Therefore,
Area of segment APB = Area of sector OAPB β Area of ΞOAB
= (231 β πππ/π βπ) cm2

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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